Module extraction plays an important role in the reuse of ontologies as well as in the simplification and optimization of some reasoning tasks such as finding justifications for entailments. In this paper the authors focus on the paper of extracting small modules for EL+ entailment based on reachability. The authors extend the current notion of forward reachability to obtain a bi-directional version, and show that the bi-directional reachability algorithm allows the authors to transform EL+ ontology into a reachability preserving context free grammar (CFG). The well known earley algorithm for parsing strings, given some CFG, is then applied to the problem of extracting minimal reachability-based axiom sets for subsumption entailments. The author has shown that each reachability-based axiom set produced by the early algorithm corresponds to a possible Minimal Axiom Set (Mena) that preserves the given entailment. This approach has two advantages - it has the potential to reduce the number of subsumption tests performed during MinA during extraction, as well to minimize the number of axioms for each such test.